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部编十年制高中数学第三册复习题三第一题:a,b 是什么实数时,a+b~(1/2)是有理数,是无理数,是虚数、是纯虚数?对这一问题现有三种不同解答:(一)安徽省教育厅教学研究室编《教学参考书》给出的解答:当 b≥0且为完全平方数,a 为有理数,或 b>0且为非完全平方数,a 为无理数且 a=-b~(1/2)时,a+b~(1/2)是有理数;当 b≥0且为完全平方数,a 为无理数,或 b>0且为非完全平方数,a 为有理数,或 b>0且为非完全平方数,a 为无理数且 a≠-b~(1/2)时,a+b~(1/2)是无理数;当 b<0时,
The first part of the ten-year high school mathematics mathematics third review question three questions: a, b What is the real number, a + b ~ (1/2) is a rational number, is an irrational number, is an imaginary number, is a pure imaginary number? There are three different solutions to the problem: (1) Answers given by the Educational Reference Book of the Educational Research Office of the Department of Education, Anhui Province: b≥0 and the number of complete squares, a is a rational number, or b>0 and is not complete The square number, a is an irrational number and a=-b~(1/2), a+b~(1/2) is a rational number; when b≥0 and is a complete square number, a is an irrational number, or b>0 and Is an incomplete square, a is a rational number, or b>0 and is an incomplete square, a is an irrational number and a≠-b~(1/2), a+b~(1/2) is an irrational number; When b<0,